Electromagnetic wave ring resonator

ABSTRACT

An electromagnetic wave ring resonator is disclosed wherein means in included for spatially rotating the electromagnetic field distribution of waves resonant therein, such rotation being about the direction of propagation of such waves. With such arrangement the electromagnetic field distribution rotating means provides a phase difference between waves of opposite polarization sense, thereby enabling the waves to resonate with different frequencies. In a four frequency laser gyroscope the electromagnetic field distribution rotating means includes a catoptric arrangement which reduces the loss, scatter and linear birefringence associated with a ring resonator included in such gyroscope.

BACKGROUND OF THE INVENTION

This invention relates generally to electromagnetic wave resonators, andmore particularly to electromagnetic wave resonators adapted for use inlaser gyroscope apparatus.

As described in U.S. Pat. No. 3,741,657 entitled "Laser Gyroscope,"Keimpe Andringa inventor, issued June 26, 1973 and assigned to the sameassignee as the present invention, a laser ring resonator supports fouroptical waves, each one of such waves having a different frequency, onepair thereof traveling in a clockwise direction and the other pairthereof traveling in a counterclockwise direction. The opticalpathlengths of the waves are such that the pair of frequencies of thewaves traveling in one direction, say the counterclockwise direction, ispositioned between the frequencies of the waves traveling in theopposite, or clockwise, direction.

Having established this frequency relationship, movement of the laserresonator, for example by rotation of the system about an axisperpendicular to the optical path, produces frequency shifts of the pairof waves propagating in one direction through the laser which areopposite to frequency shifts of the waves moving in the oppositedirection through the laser. This, in turn, produces changes in thefrequency separation between the lower frequencies of each of saidpairs. The difference between such changes is, substantially, a linearfunction of the rate of said rotation and the relative sense of suchdifference is indicative of the direction of said rotation.

As described in the referenced U.S. Pat. No. 3,741,657, such frequencyseparation results from disposing in the path of the waves apolarization dispersive structure which comprises a Faraday rotator anda crystal rotator. The crystal rotator is an anisotropic medium whichrestricts the type of polarization of the waves which may be supportedin the ring laser to substantially circular polarization and alsoprovides a different optical pathlength for right-hand sense circularlypolarized waves than for left-hand sense circularly polarized waves. TheFaraday rotator is a nonreciprocal device and provides different timedelays to waves of each polarization sense passing in the laser ring inone direction from those of such polarization sense passing in theopposite direction. The combination of the crystal rotator and Faradayrotator provides the four frequency relationship discussed above.

While the described polarization dispersive structure has been foundsatisfactory in many applications, the use of a crystal rotatorincreases loss and scatter imparted to the propagating waves andintroduces linear birefringence to the ring resonator thereby reducingthe accuracy of a laser gyroscope using such polarization dispersivestructure.

SUMMARY OF THE INVENTION

According to the present invention an electromagnetic wave ringresonator includes means for spatially rotating the electromagneticfield distribution of electromagnetic waves resonant therein about thedirection of propagation of such waves. With such arrangement suchrotating means provides a phase difference between waves of oppositepolarization sense thereby enabling such waves to resonate in suchresonator with different frequencies.

In a preferred embodiment a laser ring resonator includes a plurality ofreflectors positioned in the path of the laser to spatially rotate theelectromagnetic field distribution of the laser waves resonant thereinand thereby provide a predetermined phase alteration to the wavesresonant therein. Such phase alteration correspondingly alters theresonant frequency of each one of such waves in the ring resonatorwithout requiring a crystal rotator in such path to alter the opticalpathlength of such laser. Since the phase alteration sense is oppositefor opposite senses of circular polarization, such arrangement enableswaves of opposite polarization sense to resonate at separatefrequencies. The reflectors are preferably oriented to provide a πradian phase difference between right and left-hand circularly polarizedwaves.

BRIEF DESCRIPTION OF THE DRAWINGS

Other and further features and advantages of the invention will becomeapparent as the description thereof progresses, reference being made tothe accompanying drawings wherein:

FIG. 1 illustrates a diagrammatic view of a ring resonator embodying theinvention;

FIGS. 2A-2C are sketches useful in understanding the invention;

FIG. 3 illustrates a diagram of operating characteristics of the systemillustrated in FIG. 1; and

FIG. 4 illustrates a diagrammatic view of an alternative embodiment of aring resonator according to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to FIG. 1 there is shown a laser gyroscope system 9 havinga laser amplifier medium 10 (here a helium-neon laser medium having agas mixture: 8 ³ He + 0.48 ²² Ne + 0.52 ²⁰ Ne. A ring laser resonatorincludes an even number of reflectors, here six reflectors 12, 14, 16,18, 20, 22 (suitably mounted, by means not shown, to the surface of aplatform 23) which produce a ring path for the laser beams. It is herenoted that, as will be described later in connection with FIG. 4, thedesired ring path may be produced by as few as four properly positionedreflectors. However, the six reflector system will first be discussed inorder to establish the principle of operation of the laser gyroscopesystem. Considering the laser beam produced at end 24 of the laseramplifier medium 10, such beam travels along the +Z direction (i.e.along the longitudinal axis of the laser amplifier medium 10) through anisotropic medium, preferably substantially free space, and is firstreflected by reflector 12. The reflector 12 has its reflecting surfaceoriented such that the laser beam is reflected vertically a distance d₁along the +Y direction to reflector 14. Reflector 14 has its reflectivesurface oriented such that the beam incident thereon becomes reflectedhorizontally a distance d₂ along the -X direction to reflector 16.Reflector 16 has its reflective surface oriented so that the beamincident thereon becomes reflected vertically a distance d₁ along the -Ydirection to reflector 18. Reflector 18 has its reflective surfaceoriented so that the beam incident thereon becomes reflectedhorizontally a distance d₃ along the -X direction to reflector 20. It ishere noted that the beam passing from end 24 of laser amplifier medium10 to reflector 12 and the beam passing from reflector 18 to reflector20 are orthogonal to each other and define a common horizontal plane 26.The surface of the platform 23 is disposed in a plane parallel to thehorizontal plane 26. Therefore, the beams passing from reflector 12 toreflector 14 to reflector 16 to reflector 18 are disposed in a verticalplane. Continuing, reflector 20 has its reflective surface oriented sothat the beam incident thereon is reflected to reflector 22, theincident beam and the reflected beam being disposed in the horizontalplane 26 and having an included angle here of 60°. Reflector 22, herehaving a concave surface to aid in concentrating the laser beam throughthe laser amplifier medium 10 (i.e. to aid in establishing a resonanttransverse mode), has its reflective surface oriented so that the beamincident thereon is reflected again along the longitudinal axis of thelaser amplifier medium 10, as shown, such incident and reflected beamsbeing disposed in the horizontal plane 26 and having an included anglehere of 30°. The distance between reflectors 22 and 12 along the +Z axisis d₄.

It is here noted that, for purposes of explanation, the followingdescription neglects the effect of 180° phase changes imparted to anelectric field component upon reflection by a reflector. Suchconsideration is appropriate here because the ring resonators describedherein include an even number of reflectors in the path of the resonantwaves and hence the effect of such phase changes cancel upon traversalof the waves through the ring resonator.

Considering the beam produced at end 24 of laser amplifier medium 10 andtraveling along the +Z axis to have an electric field component E₁,disposed along the +X axis, such electric field component remains alongthe +X axis after reflection by reflector 12, then becomes orientedalong the -Y axis to the electric field component E₁ " because ofreflector 14, then becomes oriented along the -X axis because ofreflector 16, then becomes oriented along the -Y axis because ofreflector 18 and remains so oriented when it returns to end 24. Theeffect of the reflectors 12-22 on the orientation of such electric fieldcomponent E₁ is to rotate into such component -90° about the beam axis(i.e. the +Z axis) to the electric field component E₁ '.

Considering now the beam produced at the end 24 of laser amplifiermedium 10 and traveling along the +Z axis to have an electric fieldcomponent, E₂, disposed along the +Y axis, such component first becomesoriented along the +Z axis (to electric field component E₂ ") because ofreflector 12, remains oriented along the +Z axis after reflections byreflectors 14, 16 and 18, then becomes disposed in the X-Z plane at a-30° angle with respect to the +X axis (to electric field component E₂"') and then, after reflection by reflector 22, becomes oriented alongthe +X axis at the end 24 to electric field component E₂ '. The effectof the reflectors 12-22 on the orientation of such electric fieldcomponent E₂ is to rotate such component -90° about the beam axis. Theeffect of a passage around the ring may thus be symbolized:

    E.sub.1 ! E.sub.1 ' = -E.sub.2

    e.sub.2 ! e.sub.2 ' = e.sub.1

the effect of reflectors 12, 14, 16, 18, 20, 22 then is to rotate theelectromagnetic field distribution of waves passing around the ringresonator -90° in the plane orthogonal to the optical path of suchwaves. The electromagnetic field distribution refers to both theintensity and direction (i.e. polarization or electric field vector) ofan electromagnetic wave at a point in space. For example, if theelectromagnetic field distribution of waves produced by the laseramplifier medium 10 has, in the plane P, isophotes (lines 25 of equalintensity) which are elliptically shaped having vertical major axes andvertically oriented electric field components 27 as represented in FIG.2A, the effect of the reflectors 12-22 is (1) to rotate theelectromagnetic field distribution so that such electric fieldcomponents and the major axis of the isophotes are oriented horizontally(as shown in FIG. 2B) and (2) to distort such distribution because ofdiffraction and because of the concave surface of reflector 22, as shownin FIG. 2C. It is noted that in order for waves to resonate, that is, bea stable mode of the ring resonator, such waves, after passing oncearound such resonator, must return to a given point with their originalelectromagnetic field distribution. However, in general, neither theshape of the isophotes nor the polarization (electric field direction)in a given plane will remain unchanged in such plane after passing oncearound the resonator. Waves having a frequency which is capable of beinga resonant frequency will acquire an intensity distribution for whichthe diffraction of the waves and the focusing of reflector 22 arebalanced so that the waves which are resonant have the same intensitydistribution upon transversal of the resonator. However, only forcircularly polarized waves is the polarization also able to return toits initial state after one traversal. Thus, the only self-consistentelectromagnetic field distribution which may exist in the resonator isthat of waves having circular polarization. The isophotes of suchresonant waves will acquire a shape which enables support of suchcircularly polarized waves in the ring resonator. Further, if thecircular polarization of such waves has a right-hand sense polarizedcomponent, i.e.

    E.sub.r = [E.sub.1 + E.sub.2 e .sup.iπ/2 ] e.sup.-iωt

the effect of the reflectors 12-22 is to transform such component into

    E.sub.r ' = [E.sub.1 ' + E.sub.2 'e .sup.iπ/2 ] e.sup.i2πL/λ e.sup.-iωt = [-E.sub.2 + E.sub.1 e.sup.iπ/2 ] e.sup.i2πL/λ e.sup.-iωt = e.sup.iπ/2 e.sup.i2πL/λ E.sub.r

where L is the length of the path around the ring, measured along thebeam axis.

If the circular polarization of such waves has a left-hand sensepolarization component, i.e.

    E.sub.l = [E.sub.1 + E.sub.2 e.sup.-iπ/2 ] e.sup.-iωt

the effect of a passage around the ring is to transform it to

    E.sub.l ' = [E.sub.1 ' + E.sub.2 ' e.sup.-iπ/2 ] e.sup.i2πL/λ e.sup.-iωt = [-E.sub.2 + E.sub.1 e.sup.-iπ/2 ] e.sup.i2πL/λ e.sup.-iωt = e.sup.-iπ/2 e.sup.i2πL/λ E.sub.l

The relative phase difference between the left and right-hand componentsis, then,

    [e.sup.iπ/2 e.sup.i2πL/λ ] / [e.sup.i2πL/λ e.sup.-iπ/2 ] = e.sup.+iπ or 180°

Further, it should be noted that the effect of reflectors 12-22 is toalter the phase of the wave passing through the resonator, here +π/2 forright-hand sense polarized waves and -π/2 for left-hand sense polarizedwaves. Because the optical path-lengths of the waves in the resonatorare the same, as neither wave passes through a medium (here neglectingthe Faraday rotator 30 in order to understand the function of reflectors12-22) to alter such optical pathlength, the phase alteration providedby such reflectors 12-22 correspondingly alters the resonant frequenciesof such waves, the resonant frequencies of the waves of different senseof polarization altering oppositely. The result is that the waves ofright-hand sense polarization will have a resonant frequency differentfrom the resonant frequency of the left-hand sense polarized waves. Thiseffect may be understood by considering a right-hand sense polarizedwave to be represented as:

    E.sub.R = R.sub.e [e.sub.R ] = X cos (βS-ωt) - Y sin (βS-ωt)

where X, Y and Z are orthogonal unit vectors, S being measured along thedirection of propagation of the wave, ω being the angular rotationalrate of the electric field vector and β = 2π f/c = 2π λ where f and λare the frequency and wavelength, respectively, of such wave and c isthe velocity of light.

In order for such wave to resonate in a resonator, without anelectromagnetic field distribution rotation means, having opticalpathlength L, β and L must satisfy the following: βL = 2nπ (where n isan integer) and hence the resonant frequencies of such waves are

    f.sub.o = nc/L

the effect of rotating the electric field vector of such a wave in themanner described above in connection with FIG. 1 is, as described, tochange the phase of such wave and hence such phase altered wave may, forright-hand sense polarization, be represented by

    E.sub.R ' = Re[e.sub.R '] = X cos(βS-ωt + π/2) -Y sin(βS-ωt + π/2)

For resonance, β and L must then satisfy

    βL + π/2 = 2nπ, and

therefore the resonant frequencies of such wave have been changed tof_(r) ' where

    f.sub.r ' = c/2πL (2nπ - π/2)

Considering left-hand sense polarized waves, it follows that suchresonant frequency will change, because of the electric field rotationdescribed above, to

    f.sub.l ' = c/2πL (2nπ + π/2)

In summary, then, a phase alteration of φ (radians) of opposite sensefor opposite polarization senses correspondingly separates the resonantfrequencies of opposite sense polarized waves by

    Δf = c/2πL (2φ)

it further follows that such reflectors 12-22 have a reciprocal effect;that is, the phase delay will be effected for waves exiting at end 24 ofthe laser amplifier medium 10 along the +Z axis, (i.e. clockwise) andfor waves entering such end 24 along the -Z axis (i.e.counterclockwise).

A conventional solid medium Faraday rotator 30, here including a fusedsilica window with a conventionally mounted permanent magnet (not shown)is suitably mounted to the platform 23 by any convenient means (notshown). Such Faraday rotator 30 is a non-reciprocal device and producesa phase delay for waves of either circular polarization sense travelingclockwise which is different from that for waves of similar polarizationtraveling counterclockwise. The combination of the reflectors 12-22 andthe Faraday rotator 30 is such that the ring resonator supports waveshaving frequencies of oscillation as shown in FIG. 3, the two waves 32,34 traveling clockwise and the two waves 36, 38 travelingcounterclockwise, the two waves traveling clockwise having oppositesense circular polarization and the two waves traveling counterclockwisealso having opposite sense circular polarizations. These frequencies areshown as positive or negative differences from the center of maximumgain frequency of the laser amplifier medium 10.

Mirror 20 is here partially transmissive (typically less than 0.1percent) to enable a portion of the waves traveling clockwise and thewaves traveling counterclockwise to pass to the stabilization system andutilization device 40. Alternatively, specular reflections from thesurfaces of the various components in the resonator may be directed, byany conventional optical means (not shown), to such stabilization systemand utilization device 40. Here such device 40 includes a differentialamplifier (not shown) to produce an electrical signal for apiezoelectric element 41 suitably affixed to the reflector 22 to controlthe position of reflector 22 thereby to maintain the four frequenciessymmetrically about the center maximum gain frequency curve of the laseramplifier medium 10 and also includes counters (not shown) for providingan indication of the rotational rate of the laser resonator about thegyroscope axis. Such stabilization system and utilization device 40 isdescribed in the referenced U.S. Pat. No. 3,741,657.

It is here noted that two different isotopes of neon are used in thelaser amplifier medium 10, i.e. ²² Ne and ²⁰ Ne. Two different isotopesof lasing medium are provided so that each one of the four wavesinteracts with a different set of the atoms of the lasing medium, i.e.atoms with different velocities, when the cavity length is stabilized tomaintain the four frequencies symmetrically about the center maximumgain curve of the laser amplifier medium. In this regard, the ²⁰ Neisotope constitutes 52% of the neon atoms in order to compensate for itslesser atomic weight. That is, in order for the maximum gain associatedwith a composite laser medium to be half way between the resonantfrequencies associated with the two isotopes, a greater percentage of ²⁰Ne is used (i.e. 52%) as compared with ²² Ne (i.e. 48%). With thisarrangement the different sets of atoms interacting with correspondingones of the four waves will have maximum isolation from each other.

The orientation of the gyroscope axis is along the vector G. Such vectorG is calculated by the following line integral:

    G = φr X dr

where dr is the direction of travel along the path at a point on suchpath and r is the position vector of such point. Considering the ringresonator described in FIG. 1, it is noted that such waves in theresonator pass in two orthogonal planes, i.e. the horizontal plane 26and the vertical plane. The area enclosed in the horizontal plane is A₁= 1/2(d₂ +d₃)d₄. The area enclosed in the vertical plane is A₂ = d₂ d₁.The gyroscope axis then is along the vector G where

    G.sub.1 = [+A.sub.1 Y - A.sub.2 Z]

referring now to FIG. 4 a laser ring resonator here includes laseramplifier medium 10 and four reflectors, i.e. reflectors 42, 44, 46, 48positioned as shown to enable such resonator to support waves havingcircular polarization and so that right-hand sense circularly polarizedwaves have a different phase alteration than the left-hand sensecircularly polarized waves, such laser amplifier medium 10 andreflectors 42-48 being suitably mounted by conventional means (notshown) to a platform 49. A Faraday rotator 30 is included to enable suchlaser resonator to support circularly polarized waves having fourdifferent frequencies thereby enabling such apparatus to be used as afour frequency laser as described in connection with FIG. 1. Also,stabilization system and utilization device 40 is included to controlthe position of reflector 42 (such reflector 42 having a piezoelectricelement 41 mounted thereto) by responding to the portion of the wavespassing through reflector 44, as discussed in connection with FIG. 1.

It is noted that the laser waves incident on and reflected by reflector42 (here having a concave surface) are disposed in a plane 45 parallelto the plane of the platform 49. Considering the waves produced at theoutput of end 43 of laser medium 10, reflector 44 directs the beamincident thereon out of the plane 45 to reflector 46. Reflector 46directs the beam incident thereon to reflector 48, the latter reflectorredirecting such beam along the longitudinal axis of the laser amplifiermedium 10 in the plane parallel to the plane of the platform 49 (asshown). That is, segments A and B are disposed in the plane parallel tothe plane of the platform 49 and segments C and D are disposed in aplane which intersects the plane of platform 49.

The reflectors 42-48 are oriented to rotate the electromagnetic fielddistribution of the waves resonant in the ring laser -π/2 radians aboutthe direction of propagation of such waves as such waves traverse thering resonator. In order to determine the proper orientation of suchreflectors it may be helpful to analyze the reflections produced bypairs of reflectors 42-48. First, considering reflectors 46 and 48, itshould be noted that the surfaces of such reflectors are disposed in twointersecting planes, 60, 62, (shown in phantom) respectively. Suchplanes intersect along a dihedral axis 64 and form a dihedral angle γ.The dihedral axis is disposed along the unit vector Γ. As is known, twosuccessive reflections of an image are equivalent to a rotation of suchimage through an angle 2γ about the dihedral axis formed by theintersecting planes in which the surfaces of such reflectors aredisposed. That is, if the normals to the surfaces of the reflectors aren₁ and n₂, respectively,

    Γsinγ = n.sub.1 X n.sub.2

Referring again to FIG. 4, reflectors 46, 48 are oriented so that thewaves passing in segment C of the ring resonator are, after reflectionby such reflectors 46, 48, directed along the longitudinal axis of thelaser medium 10 when such waves pass in segment A (between reflectors 42and 48) of such resonator (as shown). With such orientation ofreflectors 46, 48 the electromagnetic field distribution of waves insegment C will, in segment A, be rotated by such reflectors 2γ degreesabout the unit vector Γ. Similarly, a dihedral angle and axis directionis associated with reflectors 42 and 46, and the electromagnetic fielddistribution of waves in segment A will, in segment C, be additionallyrotated in accordance with such angle and axis direction. In order toeffectuate a -π/2 radian rotation of the electromagnetic fielddistribution about the direction of propagation thereby to provide a πradian phase difference between right and left-hand circularly polarizedwaves, such reflectors 42-48 may have the following orientations:

    ______________________________________                                                 Direction Cosine of                                                           Normal to Surface of                                                          Reflector                                                            Reflector  X Axis     Y Axis     Z Axis                                       ______________________________________                                        42          0.866413  -.499328    0.0                                         44          .003688    .999298    .037273                                     46         -.209766   -.722611   -.658659                                     48         -.769676   +.164503   +.616877                                     ______________________________________                                    

It is noted that with such orientation reflectors 42 and 44 rotate theelectromagnetic field distribution of propagating waves of one circularpolarization sense -4.300 degrees and reflectors 46, 48 rotate theelectromagnetic field distribution of such waves -85.700°, the totalrotation being -90°.

In such configuration, segment A is here 15.7 centimeters (cm.).

The optical pathlength around the ring resonator is here 50 cm..Therefore, because the intermode spacing for resonant modes (for wavesof a particular polarization), Δν, is given by Δν = c/1, where c is thevelocity of light and 1 is the optical pathlength. Δν here equals 600MHz. Because the reflectors 42-48 are arranged to provide a 180° phasedifference between oppositely polarized waves, the frequency separationbetween such waves of opposite polarization is 300 MHz, that is, halfthe intermode spacing, i.e. Δν/2. It is noted that the 180° phasedifference provides maximum separation between such oppositely polarizedwaves. Further, such separation varies from zero to such maximum as thephase difference varies from 0° to 180°. As the phase differenceincreases from 180° to 360° the separation correspondingly varies fromsuch maximum back to zero.

It is now readily apparent from the foregoing that the catoptricarrangement used to rotate the electromagnetic field distribution of thewaves propagating through the ring resonator to establish circularlypolarized waves of opposite polarization sense, each having a differentresonant frequency, reduces the loss and scatter associated with theresonator when compared to an arrangement which includes an anisotropiccrystal rotator to establish such different resonant frequencycircularly polarized waves. Further, such catoptric arrangement reducesthe amount of linear birefringence in the resonator by removing theanisotropic crystal rotator and hence reduces the degree of ellipticityresulting therefrom on the propagating waves as compared with suchanisotropic crystal rotator. Misalignment in the optic axis of of suchrotator may give rise to an undesirable residual ellipticity. Suchresidual ellipticity causes undesirable instabilities in a ringresonator having such crystal rotator. The catoptric system hereindescribed has thereby effectively eliminated this source of residualellipticity and therefore reduces this instability. Further removal ofthe anisotropic medium of the crystal rotator eliminates theFizeau-Fresnel drag effect on waves passing through such medium. Stillfurther, the gain of the resonator is improved by elimination of theloss attributable to the two relatively lossy anti-reflection coatingsgenerally used on the surfaces of a crystal rotator.

Having described preferred embodiments of the invention, it is nowevident that other embodiments incorporating these concepts may be used.For example, other lasing media including other mixtures of neonisotopes may be used for the laser amplifier medium 10. It shouldtherefore be clearly understood that the details of such embodiments areset forth by way of example only and it should be understood that itwill now be readily apparent to those of skill in the art that variouschanges in form and detail thereof may be made therein without departingfrom the spirit and scope of the invention as defined by the appendedclaims.

What is claimed is:
 1. In combination:(a) an electromagnetic wave ringresonator wherein resonant electromagnetic waves propagate through anonsolid medium; (b) means, included in such ring resonator, forspatially rotating the electromagnetic field distribution of theresonant electromagnetic waves as such waves pass through the nonsolidmedium about the direction of propagation of such waves to enable theelectromagnetic waves in such resonator to resonate with differentfrequencies; and (c) means for producing different phase delays to theelectromagnetic waves having the same polarization state propagating inthe resonator in opposite directions.
 2. The combination recited inclaim 1 wherein the rotating means includes a plurality of reflectorsarranged to provide a phase difference between circularly polarizedelectromagnetic waves of opposite polarization senses to enable suchwaves of opposite polarization senses to resonate in such ring resonatorwith different frequencies.
 3. The combination recited in claim 2wherein such ring resonator includes an isotropic medium and whereinsuch rotating means rotates the electromagnetic field distribution ofsuch resonant electromagnetic waves as such waves pass through suchisotropic medium.
 4. The combination recited in claim 3 wherein suchrotating means includes a catoptric system for directing theelectromagnetic waves through the isotropic medium.
 5. The combinationrecited in claim 4 wherein a section of such resonant electromagneticwaves is disposed in a first plane and a second section of such resonantelectromagnetic waves is disposed in a second, intersecting plane. 6.The combination recited in claim 5 including a nonreciprocal means forestablishing four different resonant frequency electromagnetic waves inthe ring resonator.
 7. The combination recited in claim 6 including alaser amplifier medium disposed in the ring resonator.
 8. Incombination:(a) an electromagnetic wave ring resonator; (b) a pluralityof reflectors, included in such resonator, for directing electromagneticwaves resonant in such resonator through a predetermined path as suchwaves pass through a nonsolid medium, one section of such path beingdisposed in a first plane and a second section of such path beingdisposed in a second, intersecting plane, such plurality of reflectorsbeing arranged to provide a phase difference between circularlypolarized waves of opposite polarization senses to enable such waves ofopposite polarization senses to resonate in such resonator withdifferent frequencies; and (c) means for producing different phasedelays to the electromagnetic waves having the same polarization sensepropagating in the resonator in opposite directions.
 9. The combinationrecited in claim 8 wherein such ring resonator includes an isotropicmedium and wherein the directing means directs the resonantelectromagnetic waves through such isotropic medium.
 10. The combinationrecited in claim 9 wherein such directing means includes a catoptricsystem.
 11. In combination:(a) an electromagnetic wave ring resonator;(b) a plurality of reflectors, included in such ring resonator, arrangedto provide a phase difference between circularly polarized waves ofopposite polarization senses to enable such waves of oppositepolarization senses to resonate in such resonator with differentfrequencies; and (c) means for providing different phase delays to theelectromagnetic waves having the same polarization sense propagating inthe resonator in opposite directions.
 12. The combination recited inclaim 11 wherein such plurality of reflectors directs electromagneticwaves resonant in such ring resonator through a predetermined path, onesection of such path being disposed in a first plane and a secondsection of such path being disposed in a second, intersecting plane. 13.The combination recited in claim 12 wherein such rotating means includesa catoptric system.
 14. In combination:(a) an electromagnetic wave ringresonator; (b) a nonsolid medium disposed in the path of circularlypolarized electromagnetic waves resonant in such ring resonator; (c)means for altering the electromagnetic field distribution of the wavespassing through such nonsolid medium to enable such circularly polarizedelectromagnetic waves to resonate with different frequencies; and (d)means for producing different phase delays to the electromagnetic waveshaving the same polarization sense propagating in the resonator inopposite directions.
 15. In a laser gyroscope wherein a ring resonatoris included to support two pairs of circularly polarized waves, thewaves of each of such pairs having opposite polarization senses, one ofsuch pairs of waves propagating around the ring resonator in a firstdirection and the other one of such pairs of waves propagating aroundsuch ring resonator in the opposite direction, each one of the waves inthe two pairs thereof having a different frequency, the improvementcharacterized by a plurality of reflectors, included in such ringresonator, arranged to provide a phase difference between waves ofopposite polarization senses to enable such waves of oppositepolarization senses to resonate at different frequencies; and more forproducing different phase delays to the electromagnetic waves having thesame polarization sense propagating in the resonator in oppositedirections.
 16. The improvement recited in claim 15 wherein such ringresonator includes an nonsolid medium and wherein such rotating meansrotates the electromagnetic field distribution of such resonant waves assuch waves pass through such nonsolid medium.
 17. The combinationrecited in claim 16 wherein such rotating means includes a catoptricsystem for directing the waves through the nonsolid medium.
 18. Thecombination recited in claim 17 wherein a section of such resonant wavesis disposed in a first plane and a second section of such waves isdisposed in a second, intersecting, plane.
 19. In a laser gyroscopewherein laser waves resonate in a ring resonator, the improvementcomprising:(a) means, included in such ring resonator, comprising aplurality of reflectors arranged to direct such waves through apredetermined path, one section of such path being disposed in a firstplane and a second section of such path being disposed in a second,intersecting plane, such plurality of reflectors being arranged toprovide a phase difference between circularly polarized waves ofopposite polarization senses to enable such waves of oppositepolarization senses to resonate in such resonator at differentfrequencies; and (b) means for providing different phase delays to theelectromagnetic waves having the same polarization sense passing aroundthe resonator in opposite directions.
 20. The improvement recited inclaim 19 wherein such waves pass through an nonsolid medium and whereinsuch means directs the waves through such medium.
 21. In a lasergyroscope wherein laser waves resonate in a ring resonator, theimprovement comprising:(a) a nonsolid medium disposed in the path of thewaves; (b) means for spatially rotating the electromagnetic fielddistribution of such waves about the direction of propagation of suchwaves as such waves pass through the nonsolid medium to enableelectromagnetic waves in such resonator to resonate at differentfrequencies; and (c) means for producing different phase delays to theelectromagnetic waves having the same polarization state propagating inthe resonator in opposite directions.
 22. The improvement recited inclaim 21 wherein such rotating means directs the waves through apredetermined path, one section of such path being disposed in a firstplane and a second section of such path being disposed in a second,intersecting, plane.
 23. The improvement recited in claim 22 wherein therotating means includes a plurality of reflectors arranged to provide aphase difference between circularly polarized waves of oppositepolarization senses to enable such waves of opposite polarization sensesto resonate in such resonator with different frequencies.
 24. In a lasergyroscope wherein laser waves resonate in a ring resonator, theimprovement comprising:(a) a nonsolid medium disposed in the path ofcircularly polarized waves; (b) means for altering the electromagneticfield distribution of the waves passing through such nonsolid medium toenable such circularly polarized waves to resonate with differentfrequencies; and (c) means for providing different phase delays to theelectromagnetic waves having the same polarization sense passing aroundthe resonator in opposite directions.